In outer space far from other objects block 1 of mass 40 kg

In outer space, far from other objects, block 1 of mass 40 kg is at position m, and block 2 of mass 950 kf is at position m. what is the (vector) gravitational force acting on block 2 due to block 1? It helps to make a sketch of the situation At 4.4 seconds after noon both blocks were at rest at the position given above. At 4.6 seconds after noon, wht is the (vector) momentum of blcok 2? At 4.6 seconds after noon, which one of the following statements is true?

Solution

(a) In outer space, far from other objects, block 1 of mass 40 kg is at position < 10, 6, 0 > m, and block 2 of mass 950 kg is at position < 20, 6, 0 > m.

Mass = m1 =40 kg

Location of m1 = vector r1=10i^+6j^

Mass = m2 =950 kg

Location of m2 = vector r2=20i^+6j^

Seperation between m2 and m1 =vector s = r1 - r2=- 10i^

Direction from m2 to m1 =unit vector =s^= - i^

Gravitation force (vector ) on block 2 due to block 1 =[Gm1m2/s^2]s^

Gravitation force (vector ) on block 2 due to block 1 =[6.67*10^-11*40*950 / 10^2](-i^)

(a) Gravitation force (vector ) on block 2 due to block 1 = [2.53*10^-7 N](-i)

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Magnitude of Gravitational force on m1 =Magnitude of Gravitational force on m2 = F = 2.53*10^-7 N

Acceleration of m2 =vector a2= F/m2= [2.53*10^-7 /950 ](-i)=[2.663 *10^ -10 m/s^2](-i)

time= t =4.6 - 4.4 =0.2 s

(b) Momentum vector of block 2 =p2 =m2v2=m2a2t=950*.2*2.663*10^-10=[5.05*10^-8kgm/s](-i)
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Magnitude of Gravitational force on m1 =Magnitude of Gravitational force on m2 = F = [2.53*10^-7 N](-i)

Acceleration of m1 = vector a1= F/m1=[ 2.53*10^-7 /40]i^ =[6.325 *10^ -9 m/s^2]i^

time = t =4.6 - 4.4 =0.2 s

(c) Momentum vector of block 1 =p1 =m1v1=m1a1t=[40*6.325*10^-9*.2 kgm/s](i) =[5.06 *10^-8kgm/s](i)

d) block1 is moving faster than block2